Effective two-mode description of a few ultra-cold bosons in a double-well potential

TL;DR

This paper develops an enhanced two-mode model for ultra-cold bosons in a double-well trap, improving accuracy over traditional models by using effective wave functions derived from the many-body system.

Contribution

The paper introduces a novel two-mode model based on effective wave functions, providing more accurate dynamics of interacting bosons in a double-well potential.

Findings

Improved model closely matches exact evolution of populations.

Enhanced accuracy within certain interaction strength limits.

Outperforms traditional two-mode models in key scenarios.

Abstract

We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more closely than the traditional two-mode model.